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T. Kitagawa (Harvard), S. Pielawa (Harvard), D. Pekker (Harvard), R. Sensarma (Harvard/JQI), V. Gritsev (Fribourg), M. Lukin (Harvard),

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Probing many-body systems of ultracold atoms

Harvard-MIT

$$ NSF, MURI, DARPA, AFOSR

Eugene Demler Harvard University

T. Kitagawa (Harvard), S. Pielawa (Harvard),

D. Pekker (Harvard), R. Sensarma (Harvard/JQI),

V. Gritsev (Fribourg), M. Lukin (Harvard),

Lode Pollet (Harvard)

Collaboration with experimental groups of

T. Esslinger, I. Bloch, J. Schmiedmayer

- Lattice modulation
- experiments with
- fermions
- Ramsey interference
- experiments in 1d

Also yesterday’s talks by Henning Moritz and Andreas Ruegg

Probing the Mott state of fermions

Expts: Joerdens et al., Nature (2008)

Greif, Tarruell, Strohmaier, Moritz, Esslinger et al.

Theory: Kollath et al., PRA (2006)

Huber, Ruegg, PRA (2009)

Sensarma et al. PRL 2009

Pollet, Pekker, Demler, unpublished

Yesterday’s talks by Henning Moritz and Andreas Ruegg

Modulate lattice potential

Lattice modulation experiments

Probing dynamics of the Hubbard model

Measure number of doubly

occupied sites

Main effect of shaking: modulation of tunneling

Doubly occupied sites created when frequency w matches Hubbard U

Lattice modulation experiments

Probing dynamics of the Hubbard model

R. Joerdens et al., Nature 455:204 (2008)

Mott gap for the charge forms at

Antiferromagnetic ordering at

Mott state

Regime of strong interactionsU>>t.

“High” temperature regime

All spin configurations are equally likely.

Can neglect spin dynamics.

Doublon production rate depends on

propagation of doublons and holes

Retraceable Path Approximation Brinkmann & Rice, 1970

preliminary data

Experimental data

courtesy of D. Greif

Spectral Fn. of single hole

Doublon Production Rate

Lattice modulation experiments. Sum rule

Ad(h) is the spectral function of a single doublon (holon)

T-independent ?

Sum Rule :

Simple model to include

temperature dependence

and trap: multiply

production rate by the

average fraction of

nearest neighbors

with opposite spins

preliminary data

courtesy of D. Greif

- Using quantum noise to study many-body dynamics

One dimensional systems in condensed matter

Non-perturbative effects of interactions:

Absense of long range order

Electron fractionalization

GaAs/AlGaAs

Heterostructures

carbon

nanotubes

1d organics

Emphasis on equilibrium properties and linear response

1D Ramsey Interferometry (Widera, et.al PRL 2008)

1d systems of ultracold atoms:

analysis of nonequilibrium dynamics

Time evolution of coherence in split condensates

S. Hofferberth et al., Nature (2007)

1

Working with N atoms improves

the precision by .

t

0

Ramsey interference

Atomic clocks and Ramsey interference:

Single mode

approximation

Gaussian distribution

of Sz

Spin squeezing: possible application

in quantum enhanced metrology

Sorensen, Moller, Cirac, Zoller, Lewensstein, …

1d systems in microchips

1d systems in optical

lattices

Two component BEC

in microchip

- Ramsey interference in 1d tubes:
- Widera et al.,
- PRL 100:140401 (2008)

Treutlein et.al, PRL 2004

Spin echo experiments

A. Widera, et al, PRL 2008

Only partial revival

after spin echo!

Expect full revival of fringes

Spin echo experiments in 1d tubes

Single mode approximation does not apply.

Need to analyze the full model

Bosonization

Tomonaga-Luttinger Hamiltonian

19

Small uncertainty in

After p/2 pulse, spins point in x direction

Initial state: squeezed state infs

Wk determined from

Short distance cut-off at spin healing length

related argument in Bistrizer, Altman, PNAS (2008)

Luttinger liquid provides good agreement with experiments.

A. Widera et al., PRL 2008. Theory: V. Gritsev

Technical noise could also

lead to the absence of echo

Need “smoking gun” signatures

of many-body decoherece

Distribution

Distribution function contains information about higher order correlations

Joint distribution function can

also be obtained

S. Hofferberth, I. Lesanovsky, T. Schumm, J. Schmiedmayer,

A. Imambekov, V. Gritsev, E. Demler, Nature Physics (2008)

Higher order correlation functions

probed by noise in interference

Short segments

|S|^2 does not changebut Sx decays

Long segments

both Sx and |S|^2 decay

Modes with λ>l leads to the decay of Sx but not |S|

Modes with λ<l leads to the decay of both Sx and |S|

- Suggested unique signatures of the multimode decoherence of Ramsey fringes in 1d
- Ramsey interferometer combined with study of distribution function is a useful tool to probe many-body dynamics
- Joint distribution functions provide simple visualization of complicated many-body dynamics